We give analytical expressions for the eigenvalues and generalized eigenfunctions of Tˆ3, the z-axis projection of the toroidal dipole operator, in a system consisting of a particle confined in a thin film bent into a...
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Main goal of the work was development of the software aimed to compute eigenvalues and eigenfunctions of regular and singular self-adjoin. Sturm-Liouville problems, with both separated and coupled boundary conditions,...
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ISBN:
(纸本)5965100647
Main goal of the work was development of the software aimed to compute eigenvalues and eigenfunctions of regular and singular self-adjoin. Sturm-Liouville problems, with both separated and coupled boundary conditions, and to approximate the continuous spectrum in the singular case. Computational algorithms of SLEIGN2 package [1] were taken as a basis for our software. SLEIGN2 code itself is based on ideas and methods of the original SLEIGN code [2].
The calculation of eigenvalues and eigenfunctions of a class of normal operators associated with hyperbolic PDEs (partial differential equations) for which no closed-form solution to the eigenproblem is known is consi...
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The calculation of eigenvalues and eigenfunctions of a class of normal operators associated with hyperbolic PDEs (partial differential equations) for which no closed-form solution to the eigenproblem is known is considered. An inverse power method is applied to this problem; it is constructed so that all calculations remain real even though the eigenvalues are imaginary. An example illustrates the practical application of the method.< >
The modified iterative method (MIM) is discussed. The MIM is a method for obtaining the completely continuous operator eigenvalues and eigenfunctions. The authors correct the formulation and demonstration of the MIM s...
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The modified iterative method (MIM) is discussed. The MIM is a method for obtaining the completely continuous operator eigenvalues and eigenfunctions. The authors correct the formulation and demonstration of the MIM substantive theorem, demonstrate the MIM correlation with a moment method and give some numerical results. The ordinary successive approximation method, which is used to calculate the first eigenvalue and its eigenfunction, consists of multiple iterations by the operator of any initial function for all vanishing next eigenfunctions in its decomposition. When the iterative process becomes stable the final result is obtained from the last two iterations. The MIM allow the use of all iterations with the initial function simultaneously to get the information about all eigenfunctions, not only about the first one. In this case there is a need for far fewer iterations to achieve a prescribed precision. It is also possible to separate each eigenfunction, even those which correspond to eigenvalues with closely placed magnitudes.
It is known that every positive solution of a one-dimensional Gel’fand problem can be written explicitly. In this paper we give exact expressions of all the eigenvalues and eigenfunctions of the linearized eigenvalue...
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We study asymptotics of the eigenvalues and eigenfunctions of the operators used for constructing multidimensional scaling (MDS) on compact connected Riemannian manifolds, in particular on closed connected symmetric s...
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For a family of elliptic operators with periodically oscillating coefficients, −div(A(·/Ε)∇) with tiny Ε > 0, we comprehensively study the first-order expansions of eigenvalues and eigenfunctions (eigenspace...
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Asymptotic eigenvalues and eigenfunctions for the Orr-Sommerfeld equation in two and three dimensional incompressible flows on an infinite domain and on a semi-infinite domain are obtained. Two configurations are cons...
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We consider the problem of estimating the eigenvalues and the integral of the corresponding eigenfunctions, associated to the Newtonian potential operator, defined in a bounded domain Ω ⊂ Rd, where d = 2, 3, in terms ...
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We investigate multiplicity and symmetry properties of higher eigenvalues and eigenfunctions of the p-Laplacian under homogeneous Dirichlet boundary conditions on certain symmetric domains RN. By means of topological ...
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